Determine the angle between the inclined plane and the horizontal

A hollow, thin-walled cylinder and a solid sphere start from rest and roll without slipping down an inclined plane of length 5 m. The cylinder arrives at the bottom of the plane 2.6 s after the sphere. Determine the angle between the inclined plane and the horizontal.

The sun's radius is 6.96 108 m, and it rotates with a period of 25.3 days. Estimate the new period of rotation of the sun if it collapses with no loss of mass to become a neutron star of radius 5.3 km.

T2/T1 = R^2/R^2 and I got 1.47 x 10^-9 days m for T2 and then I converted it and get 1.27 x 10^-4ms
Figure 10-45 shows a hollow cylindrical tube of mass M = 0.8 kg and length L = 1.9 m. Inside the cylinder are two masses m = 0.4 kg, separated a distance = 0.6 m and tied to a central post by a thin string. The system can rotate about a vertical axis through the center of the cylinder. The system rotates at such that the tension in the string is 108 N just before it breaks.

I have no idea if this is right or wrong. You didn't say what
"phida" means.

The sun's radius is 6.96 108 m, and it rotates with a period of 25.3 days. Estimate the new period of rotation of the sun if it collapses with no loss of mass to become a neutron star of radius 5.3 km.

T2/T1 = R^2/R^2 and I got 1.47 x 10^-9 days m for T2 and then I converted it and get 1.27 x 10^-4ms

Okay, you used "conservation of angular momentum". Looks good.

Figure 10-45 shows a hollow cylindrical tube of mass M = 0.8 kg and length L = 1.9 m. Inside the cylinder are two masses m = 0.4 kg, separated a distance = 0.6 m and tied to a central post by a thin string. The system can rotate about a vertical axis through the center of the cylinder. The system rotates at such that the tension in the string is 108 N just before it breaks.

What is the question? In any case, you don't say what the radius of the cylinder is.